Thermodynamics & stoichiometry Lecture-G-L6-1home.agh.edu.pl/~lstepien/Gasification/Lectures/L6-1.pdf · Lecture-G-L6-1 Marek Sciazko ... or kg/kmol is the mass of one mole of the

Thermodynamics & stoichiometry Lecture-G-L6-1

Marek Sciazko

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Thermodynamics

• Thermodynamics is the study of the effects of work, heat, and energy on a system

• Thermodynamics is only concerned with macroscopic (large-scale) changes and observations

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Getting Started

• All of thermodynamics can be expressed in terms of four quantities

– Temperature (T)

– Internal Energy (U)

– Entropy (S)

– Heat (Q)

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The first law

• The first law of thermodynamics is an extension of the law of conservation of energy

• •The change in internal energy of a system is equal to the heat added to the system minus the work done by the system

– ΔU = Q -W

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Definition

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Process Terminology

• Adiabatic –no heat transferred

• Isothermal –constant temperature

• Isobaric –constant pressure

• Isochoric –constant volume

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Thermodynamic system and control volume

• We take the following definitions:

– Thermodynamic system: an object and quantity under investigation,

– Surroundings: everything external to the system,

– System boundary: interface separating system and surroundings, and

– Universe: combination of system and surroundings

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System

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Phase transition

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Thermal equations of state

• Thermal equation of state: an equation which gives the pressure as a function of two independent state variables. An example is the general form:

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Ideal gas law

• Ideal gas law: This equation is fundamentally stated as


For air


Material Balances on Reactive Processes

• Material balances on processes involving chemical reactions may be solved by applying:

– Molecular Species Balance – a material balance equation is applied to each chemical compound appearing in the process.

– Atomic Species Balance – the balance is applied to each element appearing in the process.

– Extent of Reaction – expressions for each reactive species is written involving the extent of reaction.


Chemical Reactions, Atoms and Molecules in Combustion

• A chemical reaction is an exchange and/or rearrangement of atoms between colliding molecules, for example:

• The atoms are conserved (they are not created or destroyed) while molecules are not conserved.

• In the above reaction H, O atoms are conserved while molecules H2, O2 and H2O are not.

• Reactant molecules (H2 and O2) are rearranged to become product (H2O) molecules. Heat is released in this process.


Amount of Substances, Mole and Mass Fractions

• Atoms and molecules are counted in amount of substances or moles. 6.023 · 1023 particles (atoms, molecules) are called one mole of the substance (Avogadro constant).


• For a mixture of species:

– where n stands for total number of moles, ni is the number

of moles of species i, and the summation extends over all the species.

• Mole fraction –yi – (mole number) of species i is:

𝑦𝑖 =𝑛𝑖𝑛


• The molar mass (molecular weight) in g/mol or kg/kmol is the mass of one mole of the species (for example: MC = 12 g/mol, MCO2

= 44 g/mol).

• The mean molar mass (molecular weight) of a mixture is:

𝑀𝑚𝑒𝑎𝑛 = 𝑦𝑖𝑀𝑖𝑖


Molecular and Elemental Balances

• For steady-state reactive processes: Input + Generation = Output + Consumption

• The generation and consumption terms in the

molecular balance equation is usually obtained from chemical stoichiometry.

• But for an atomic balance, for all cases

Input = Output


Dehydrogenation of Ethane

• Consider the dehydrogenation of ethane in a steady-state continuous reactor,


• Total Balance: Input = Output

• Molecular Species Balance: – C2H6: Input – Consumed = Output

– C2H4: Generated = Output

– H2: Generated = Output

• Atomic (Elemental) Species Balance: – C-Balance: Input = Output

– H-Balance: Input = Output


Independent reactions in gasification?

• C + O2 = CO2

• C + CO2 = 2 CO

• C + H2O = CO2 + H2

• CO + H2O = CO2 + H2


Degrees of Freedom of Analysis for Reactive Processes

• Molecular Species Balance

+ No. identified/labeled unknowns

+ No. independent chemical reactions

– No. of independent molecular species

– No. other equations relating unknown variables

------------------------------------------------------------------

= No. degrees of freedom


• Atomic Species Balance

+ No. identified/labeled unknowns

– No. independent atomic species

– No. of independent nonreactive molecular species

– No. other equations relating unknown variables

------------------------------------------------------------------

= No. degrees of freedom


Independent Chemical Reactions, Molecular and Atomic Species

• Chemical reaction: A chemical reaction is independent if it cannot be obtained algebraically from other chemical reactions involved in the same process.

• Molecular Species: If two molecular species are in the same ratio to each other wherever they appear in a process, then these molecular species are not independent.

• Atomic Species: If two atomic species occur in the same ratio wherever they appear in a process, balances on those species will not be independent equations.



• Consider the following reactions:

A =======> 2B

B =======> C

A =======> 2C

• Are these chemical reactions independent?



• Consider a continuous process in which a stream of liquid carbon tetrachloride (CCl4) is vaporized into a stream of air.


• Molecular Species Analysis

– Total: 3 (O2, N2, CCl4)

– Independent: 2 (O2 or N2, CCl4)

• Atomic Species Analysis

– Total: 4 (O, N, C, Cl)

– Independent 2 (O or N, Cl or C)


Example. Production of Chlorine

• In a process for the manufacture of chlorine, HCl and O2 react to form Cl2 and H2O.

• Sufficient air (21 mole% O2, 79% N2) is fed to provide 35% excess oxygen and the fractional conversion of HCl is 85%.

• Determine the amount of air required per mole of HCl fed into the process.

• Calculate the mole fractions of the product stream components using: a. molecular species balances b. atomic species balances c. extent of reaction


• Identify the components of the product stream:

– HCl since not all will be converted (based on fractional conversion)

– O2 since it is supplied in excess

– N2 it goes with the O2 in air but not consumed during the reaction

– Cl2 produced during the process

– H2O produced during the process



• To get mole fractions of components in the product stream: yi = ni/nt

• For the identified components: yHCl = n2/nt

yO2 = n3/nt

yN2 = n4/nt

yCl2 = n5/nt

yH2O = n6/nt

where nt = n2 + n3 + n4 + n5 + n6


DEGREES OF FREEDOM ANALYSIS: Molecular Balance


• HCl Balance: Input – Consumed – Output = 0

(100 mol) – 0.85(100 mol) – n2 = 0

n2 = 15 mol HCl

• O2 Balance: Input – Consumed – Output = 0

(33.75 mol) – 85 mol HCl react (0.5/2) – n3 = 0

n3 = 12.5 mol O2

• N2 Balance: Output = Input

n4 = 160.7 mol air (0.79 mol N2/1 mol air)

n4 = 127 mol N2


• Cl2 Balance: Generated – Output = 0

85 mol HCl react (1/2) – n5 = 0

n5 = 42.5 mol Cl2

• H2O Balance: Generated – Output = 0

85 mol HCl react (1/2) – n6 = 0

n6 = 42.5 mol H2O


Calculation for mole fractions:


DEGREES OF FREEDOM ANALYSIS: Atomic Balance


• From % excess O2 ======> n1

• From fractional conversion ======> n2

• Atomic Species Balance:

H-Balance: 100(1) = n2 + 2n6

O-Balance: n1(0.21)(2) = 2n3 + n6

Cl-Balance: 100(1) = n2 + 2n5

N-Balance: n1(0.79)(2) = 2n4


STOICHIOMETRY OF HYDROCARBONS OXIDATION


BURNING OF STOICHIOMETRIC METHANE MIXTURE IN AIR


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Thermodynamics & stoichiometry Lecture-G-L6-1home.agh.edu.pl/~lstepien/Gasification/Lectures/L6-1.pdf · Lecture-G-L6-1 Marek Sciazko ... or kg/kmol is the mass of one mole of the